On this page
Specify every overlap needed for the calculation
The fictional universe has 1,200 distinct issuers. List A contains 38, B contains 61 and C contains 22. Exactly four issuers belong to both B and C. A has no overlap with either other list, and there is no three-way overlap. Without these last conditions, the three counts and one overlap would not determine the union.
Count the union once
Adding the list lengths gives 121 entries, but the four shared B–C issuers are each counted twice. Subtract their extra appearances once: 38 + 61 + 22 − 4 = 117 unique exclusions.
| Step | Count |
|---|---|
| List memberships before deduplication | 121 |
| Extra appearances from the B–C overlap | 4 |
| Unique excluded issuers | 117 |
| Eligible issuers: 1,200 − 117 | 1,083 |
Check the no-overlap shortcut
Subtracting 121 directly from the universe gives 1,079, four too few eligible issuers. The error is double-counting the four shared exclusions. It is not evidence that a fourth exclusion list exists.
Extend the idea to three overlapping lists
If every pair can overlap, inclusion–exclusion subtracts all three pairwise intersections and then adds the three-way intersection back once. In a real worksheet, stable issuer identifiers are preferable to company-name matching because spelling differences and subsidiaries can obscure duplicate records.